Matching point locations: Relative translation, preserving surrounding geometry
Multiple objects

This can be done with a combination of transform snapping and 3D cursor snapping.


Snap the cursor the the point vertex by selecting it in edit mode (&#8633; Tab) and pressing &#8679; ShiftS> Cursor to selected:


Set the pivot point to 3D cursor (.)
Set the snap element to vertex and the snap target to Center in 3D view > Header:


In object mode, grab the pointer object and move it over the target vertex while holding &#9096; Ctrl:






Single mesh

If everything is in the same mesh, you don't even need to use the 3D cursor:


Select the geometry you want to move, making sure the vertex on the tip is active (last selected, appears white):


Set the snap target to Active:


Snap away by holding &#9096; Ctrl. 



Note that you can also enable snapping without holding &#9096; Ctrl by clicking the magnet icon in 3D view > header, then things will snap by default and holding &#9096; Ctrl will make them not snap.